In this paper,two speech enhancement systems with supergaussian speech modeling are presented. The clean speech components are estimated by Minimum-Mean-Square-Error (MMSE) es-timator under the assumption that the DCT coefficients of clean speech are modeled by a Laplacian or a Gamma distribution and the DCT coefficients of the noise are Gaussian distributed. Then,MMSE estimators under speech presence uncertainty are derived. Furthermore,the proper estimators of the speech statistical parameters are proposed. The speech Laplacian factor is estimated by a new deci-sion-directed method. The simulation results show that the proposed algorithm yields less residual noise and better speech quality than the Gaussian based speech enhancement algorithms proposed in recent years.